Physics quiz question: step-up transformer output voltage

Physics 205B Quiz 6, spring semester 2019
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 20.34

The primary coil of a transformer has 400 turns; the secondary coil has 1,000 turns. An alternating current is sent through the primary coil with an input emf of 17 V. The output emf in the secondary coil is:
(A) 6.8 V.
(B) 10 V.
(C) 26 V.
(D) 43 V.

Correct answer: (D)

Given: N₁ = 400 turns, N₂ = 1,000 turns, and ε₁ = 17 V.

Since ε₂/ε₁ = N₂/N₁ = I₁/I₂, then:

ε₂ = ε₁·(N₂/N₁) = (17 V)·(1,000/400) = 42.5 V,

which was expected to be higher than the input emf, as this is a step-up transformer (more turns in the secondary coil than the primary coil).

(Response (A) is ε₁·(N₁/N₂); response (B) is ε₁*(N₂ – N₁)/N₂; response (C) is ε₁·(N₂ – N₁)/N₁.

Student responses
Sections 30882, 30883
Exam code: quiz06riQ1
(A) : 4 students
(B) : 1 student
(C) : 2 students
(D) : 31 students

Success level: 82%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.25